Abstract
We consider risk measurement in controlled partially observable Markov processes in discrete time. We introduce a new concept of conditional stochastic time consistency and we derive the structure of risk measures enjoying this property. We prove that they can be represented by a collection of static law invariant risk measures on the space of function of the observable part of the state. We also derive the corresponding dynamic programming equations. Finally we illustrate the results on a machine deterioration problem.
Original language | English (US) |
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Pages (from-to) | 161-184 |
Number of pages | 24 |
Journal | Mathematical Methods of Operations Research |
Volume | 88 |
Issue number | 2 |
DOIs | |
State | Published - Oct 1 2018 |
All Science Journal Classification (ASJC) codes
- Software
- General Mathematics
- Management Science and Operations Research
Keywords
- Dynamic programming
- Dynamic risk measures
- Partially observable Markov processes
- Time consistency